## Reactive, Generative and Stratified Models of Probabilistic Processes (1990)

Venue: | Information and Computation |

Citations: | 152 - 6 self |

### BibTeX

@ARTICLE{Glabbeek90reactive,generative,

author = {Rob J. Van Glabbeek and Scott A. Smolka and Bernhard Steffen},

title = {Reactive, Generative and Stratified Models of Probabilistic Processes},

journal = {Information and Computation},

year = {1990},

volume = {121},

pages = {130--141}

}

### Years of Citing Articles

### OpenURL

### Abstract

ion Let E; E 0 be PCCS expressions. The inter-model abstraction rule IMARGR is defined by E ff[p] \Gamma\Gamma! i E 0 =) E ff[p= G (E;fffg)] ae \Gamma\Gamma\Gamma\Gamma\Gamma\Gamma! i E 0 This rule uses the generative normalization function to convert generative probabilities to reactive ones, thereby abstracting away from the relative probabilities between different actions. We can now define 'GR ('G (P )) as the reactive transition system that can be inferred from P 's generative transition system via IMARGR . By the same procedure as described at the end of Section 3.1, 'GR can be extended to a mapping 'GR : j GG ! j GR . Write P GR ¸ Q if P; Q 2 Pr are reactive bisimulation equivalent with respect to the transitions derivable from G+IMARGR , i.e. the theory obtained by adding IMARGR to the rules of Figure 7. The equivalence GR ¸ is defined just like R ¸ but using the cPDF ¯GR instead of ¯R . ¯GR is defined by ¯GR (P; ff; S) = X i2I R (=I G ) fj p i j G+ I...

### Citations

3204 |
Communication and Concurrency
- Milner
- 1989
(Show Context)
Citation Context ... purposes, the classical nonprobabilistic model, we present the following: ffl a structural operational semantics of PCCS, given as a set of inference rules in the style of Plotkin [Plo81] and Milner =-=[Mil89]-=-. For each model, these inference rules determine a semantic mapping from the set of PCCS expressions to a particular domain of probabilistic labeled transition systems. We denote these mappings as 'N... |

1286 | A structural approach to operational semantics
- Plotkin
- 1981
(Show Context)
Citation Context ...and, for comparison purposes, the classical nonprobabilistic model, we present the following: ffl a structural operational semantics of PCCS, given as a set of inference rules in the style of Plotkin =-=[Plo81]-=- and Milner [Mil89]. For each model, these inference rules determine a semantic mapping from the set of PCCS expressions to a particular domain of probabilistic labeled transition systems. We denote t... |

655 | Concurrency and automata on infinite sequences - Park - 1981 |

403 | Bisimulation through probabilistic testing
- Larsen, Skou
- 1991
(Show Context)
Citation Context ...ent fails. In response to a successful experiment, the process makes an internal state transition and is then ready for further experimentation. The reactive model has been adopted by Larsen and Skou =-=[LS91]-=- for probabilistic processes : a button-pressing experiment succeeds, with probability 1, or else fails. If successful, the process makes an internal state transition according to a probability distri... |

311 |
Calculi for Synchrony and Asynchrony
- Milner
- 1983
(Show Context)
Citation Context ...in [SS90]. Summary of Technical Results We will be working within the framework of PCCS, a specification language for probabilistic processes introduced in [GJS90]. PCCS is derived from Milner's SCCS =-=[Mil83]-=- by replacing the operator of nondeterministic process summation with a probabilistic counterpart. Several PCCS expressions have appeared above, which should give the flavor of the language. 3 For eac... |

125 |
A probabilistic powerdomain of evaluations
- Jones, Plotkin
- 1989
(Show Context)
Citation Context ...lassical testing theory of De Nicola and Hennessy are demonstrated. 6 Similar connections are made by Yi and Larsen in [YL92] for a model of probabilistic processes based on [HJ90]. Jones and Plotkin =-=[JP89]-=- investigate a probabilistic powerdomain of evaluations, which they use to give the semantics of a language with a probabilistic parallel construct. Finally, Seidel [Sei92] uses conditional probabilit... |

96 | Specification and refinement of probabilistic processes - Jonsson, Larsen - 1991 |

95 |
A calculus for communicating systems with time and probabilities
- Hansson, Jonsson
- 1985
(Show Context)
Citation Context ...ion, except for [JS90], where also probabilistic versions of trace, failure and readiness equivalences and congruences are studied. The interplay between time and probability has been investigated in =-=[HJ90, Low91]-=-. Larsen and Skou [LS91] have examined the reactive model in the setting of testing. They exhibit a testing algorithm that, with probability 1 \Gamma ffl, where ffl is arbitrarily small, can distingui... |

94 | Algebraic reasoning for probabilistic concurrent systems
- Giacalone, Jou, et al.
- 1990
(Show Context)
Citation Context ... in modeling priority is examined carefully in [SS90]. Summary of Technical Results We will be working within the framework of PCCS, a specification language for probabilistic processes introduced in =-=[GJS90]-=-. PCCS is derived from Milner's SCCS [Mil83] by replacing the operator of nondeterministic process summation with a probabilistic counterpart. Several PCCS expressions have appeared above, which shoul... |

69 |
Equivalences, congruences, and complete axiomatizations for probabilistic processes
- Jou, Smolka
- 1990
(Show Context)
Citation Context ...a includes [LS92] (in a reactive setting), [JS90, JL91, BBS92] (in a generative setting) and [SS90, Tof90b] (in a stratified setting). All these papers consider probabilistic bisimulation, except for =-=[JS90]-=-, where also probabilistic versions of trace, failure and readiness equivalences and congruences are studied. The interplay between time and probability has been investigated in [HJ90, Low91]. Larsen ... |

66 | Axiomatizing probabilistic processes: ACP with generative probabilities - Baeten, Bergstra, et al. - 1995 |

60 |
Testing Probabilistic and Nondeterministic Processes
- Wang, Larsen
- 1992
(Show Context)
Citation Context ...erative processes as well (but with generative tests); close connections to the classical testing theory of De Nicola and Hennessy are demonstrated. 6 Similar connections are made by Yi and Larsen in =-=[YL92]-=- for a model of probabilistic processes based on [HJ90]. Jones and Plotkin [JP89] investigate a probabilistic powerdomain of evaluations, which they use to give the semantics of a language with a prob... |

47 |
A calculus of communicating systems, LNCS92
- Milner
- 1980
(Show Context)
Citation Context ...Introduction In the reactive model [Pnu85] of classical concurrency theory, a process reacts to stimuli presented by its environment. A mechanistic view of the reactive model has been given by Milner =-=[Mil80]-=- in terms of button pushing experiments. The environment or observer experiments on a process by attempting to depress one of several buttons that the process possesses as its interface to the outside... |

39 | Compositional verification of probabilistic processes - Larsen, Skou - 1992 |

37 |
Probabilistic communicating processes
- Seidel
- 1995
(Show Context)
Citation Context ...on [HJ90]. Jones and Plotkin [JP89] investigate a probabilistic powerdomain of evaluations, which they use to give the semantics of a language with a probabilistic parallel construct. Finally, Seidel =-=[Sei92]-=- uses conditional probability measures to give a semantics to a probabilistic extension of CSP. 2 Syntax of PCCS As in SCCS, the atomic actions of PCCS form a multiplicative structure (Act; \Delta) th... |

31 |
Linear and Branching Structures in the Semantics and Logics of Reactive Systems
- PNUELI
- 1985
(Show Context)
Citation Context ...ely probabilistic branching structure. Moreover the classical nonprobabilistic model is derivable from each of these models by abstraction from all probabilities. 1 Introduction In the reactive model =-=[Pnu85]-=- of classical concurrency theory, a process reacts to stimuli presented by its environment. A mechanistic view of the reactive model has been given by Milner [Mil80] in terms of button pushing experim... |

18 |
Testing Equivalences for Probabilistic Processes
- Christoff
- 1990
(Show Context)
Citation Context ...s P and Q are bisimilar, then there is an assignment of probabilities to the edges of P and Q, yielding reactive processes P 0 and Q 0 such that P 0 and Q 0 are probabilistically bisimilar. Christoff =-=[Chr90]-=- also considers the testing of probabilistic processes. He proposes three probabilistic trace-based testing equivalences for generative processes using nondeterministic tests. Cleaveland et al. [CSZ92... |

17 | B.: Priority as extremal probability
- Smolka, Steffen
(Show Context)
Citation Context .... Thus process R can only be executed in a restriction context that excludes P and Q. Zero probabilities are not considered in this paper, but their role in modeling priority is examined carefully in =-=[SS90]-=-. Summary of Technical Results We will be working within the framework of PCCS, a specification language for probabilistic processes introduced in [GJS90]. PCCS is derived from Milner's SCCS [Mil83] b... |

14 |
A remark on bisimulation between probabilistic processes
- Bloom, Meyer
- 1989
(Show Context)
Citation Context ...g of testing. They exhibit a testing algorithm that, with probability 1 \Gamma ffl, where ffl is arbitrarily small, can distinguish processes that are not probabilistically bisimilar. Bloom and Meyer =-=[BM89]-=- further show that if nondeterministic bounded-branching processes P and Q are bisimilar, then there is an assignment of probabilities to the edges of P and Q, yielding reactive processes P 0 and Q 0 ... |

13 | Prioritized and probabilistic models of timed CSP - Lowe - 1994 |

2 |
Proof Methods and Pragmatics for Parallel Programming
- Tofts
- 1991
(Show Context)
Citation Context ...d model the only choice mechanism is probabilistic. Only the probability transitions need to be indexed. This bi-structured approach to operational semantics was (to our knowledge) first presented in =-=[Tof90a]-=- to give a semantics for a timed version of CCS. Note that no PCCS expression admits both action and probability transitions. Thus the set of PCCS processes is partitioned into action processes (admit... |

1 |
Zwarico (1992): Testing preorders for probabilistic processes
- Cleaveland, Smolka
(Show Context)
Citation Context ...Chr90] also considers the testing of probabilistic processes. He proposes three probabilistic trace-based testing equivalences for generative processes using nondeterministic tests. Cleaveland et al. =-=[CSZ92]-=- investigate the testing of generative processes as well (but with generative tests); close connections to the classical testing theory of De Nicola and Hennessy are demonstrated. 6 Similar connection... |

1 | Tofts (1990): A synchronous calculus of relative frequency - N |